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Plasma generated by hypersonic aerocraft is one of the research subjects in computational electromagnetics. When the aerocraft flies at an ultra-high speed in the near space, plasma sheath will be generated in the surroundings and it will trigger varying changes in aerocraft radar electromagnetic scattering properties. Plasma sheath brings about tremendous impacts on the communication between the aerocraft and the outside world, and even ends with "blackout effects" to interrupt communication in severe cases. The interplay between the plasma sheath and the electromagnetic wave involves multiple disciplines covering aerodynamics, plasma sheath physics, and electromagnetic field theory. Therefore, it is challengeable to build a rigorous numerical modeling of the plasma sheath. In this paper, the latest technologies in the electromagnetic simulation of hypersonic aerocraft with plasma sheath are reviewed. Applied cases review and illustrate extensive approaches from approximate calculations to accurate calculations, including analytical methods, differential equation methods, integral equation methods and high-frequency approximation methods. The paper assesses the RCS of electromagnetic wave in analyzing the electromagnetic scattering problem in plasma. With the considerations the reality of electromagnetic simulation and future challenges, the paper talks about the efficiency, advantages and disadvantages of these approaches in simulating hypersonic aerocraft targets.

During the flight of a hypersonic vehicle, a plasma sheath will be produced around the vehicle due to the effect of the shock layer. Because the plasma sheath will absorb, reflect, and scatter electromagnetic waves, which causes the communication signal to be attenuated or even interrupted, forming a communication ``blackout.'' In this article, the plasma sheath is illuminated by a high-power microwave (HPM) when the hypersonic vehicle is in the state of thermodynamic equilibrium and chemical nonequilibrium. Thus, the parameters of the plasma sheath change because of absorbing the energy of the HPM and then affect the electromagnetic characteristics of the plasma sheath. Aiming at the interaction between the HPM and the plasma sheath, we propose a multiphysics coupling model of fluid field and electromagnetic field, which provides a way of thinking for the interaction of electromagnetic and fluid coupling. Furthermore, through this multiphysics coupling method, it is found that the HPM illuminates into the plasma sheath, the ability of low-frequency electromagnetic waves to pass through the plasma sheath will be improved within a specific time window, which provides a possibility to enhance the communication blackout problem. Since the primary purpose of this article is to reveal the multiphysics field method and its related phenomena, both theoretical derivations and numerical examples are only presented in the 2-D space.

The plasma sheath will be generated on the surface of the reentry object due to the effect of aerodynamic thermoionization, causing multi-component signals with Doppler frequency components in the radar echo. This situation will further result in the appearance of false targets that seriously affect the detection of reentry targets by radar, causing positioning errors and even tracking losses. In this paper, the echo signal model of the plasma-sheath-covered reentry target is established, and the multi-domain characteristics of the echo signal in terms of time, time-frequency and range are analyzed, revealing the influence mechanism of plasma sheath on radar detection of reentry target. Through range-period analysis, the influence of intra-pulse Doppler frequency caused by plasma sheath is determined, as well as inter-pulse Doppler frequency on target range measurement. Theoretical analyses conducted in this study are verified by simulation results, laying theoretical foundation for effective detection and reliable tracking of plasma-sheath-covered reentry targets.

Radio frequency (RF) blackout occurs during radio attenuation measurement C (RAMC) vehicle reentry due to the attenuation effect of the plasma sheath on the communication signal. In recent years, the mitigation mechanism of chemical reaction for RF blackout problem has gradually been studied numerically and experimentally. However, the effect of non-ionization reaction rate has been ignored because it does not directly involve the generation of electrons. In the present study, the influence of non-ionizing reaction rate on the plasma generation mechanism and EM wave attenuation was numerically solved by the plasma flow and multilayer transmission model. According to the simulation results, only the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O has a significant effect on the electron number density in all non-ionizing reactions, and the degree of influence is less than the ionization reaction rate. The EM wave attenuation decreases with the decrease of the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O . When the reaction rate is reduced by 25 times, the maximum attenuation of electromagnetic wave can be reduced by 12 dB. Finally, a potential scheme by reducing the reaction rate of $$NO \rightleftharpoons N + O$$ N O ⇌ N + O was proposed to mitigate the RF blackout problem.

The main goal here is to study theoretically the formation of plasma sheath in an inhomogeneous dusty plasma. The effect of weak ionization of the dust grains as similar to the Townsend discharge has been incorporated to see how it influences the evolution of sheath. Sheath equation has been derived to describe the properties of sheath structures analytically and numerically. It has shown that the ionization along with the inhomogeneity affects significantly the growth of sheath which has been highlighted elaborately for some typical plasma parameters. After getting well defined sheath region, dynamical behaviour of levitated dust grains into the sheath has been studied. The totality of the findings has been centred around the estimation of dust surface potential, dust sizes along with the generation of net force on dust grains. Both inhomogeneous and ionization effects allow the dust grains in acquiring different potential to sustain equilibrium in different places. As a result of this, nebulons and the dust cloudlike structures are electrically charged.

During the reentry process of a spacecraft, a plasma sheath will attenuate and distort the amplitude and phase of the transmitting electromagnetic (EM) waves, influencing signal reception and measurement accuracy of the direction of wave arrival of the spacecraft-borne array antenna, by which the spacecraft communication and guidance system may be affected. To solve this problem, based on the space distribution characteristics of plasma sheath flow field, an EM simulation model of an array antenna under plasma sheath is established, and EM simulations related to field propagation across plasma sheath and radome are performed. Then, the array signal model is constructed by extracting the field strength data at the array element. Several spatial spectrum estimation methods are conducted to calculate the direction of arrival of an EM wave incident on the array antenna. By comparing the direction of the incoming wave in free space with the estimated direction after propagating through the plasma sheath, the direction-finding error of the spacecraft-borne array under the plasma sheath is obtained, and the cause of the error is analyzed. With compensation information, the results of the proposed method can enable higher target-tracking accuracy for the spacecraft guidance system.

A narrow region having sharp gradients in physical parameters is formed whenever plasma comes into contact with a material wall. In this work, the temporal velocity variation of ions in such a sheath has been studied in the presence of an external oblique magnetic field. The Lorentz force equation has been solved for the given boundary conditions using Runge-Kutta method. In order to satisfy the Bohm criterion, ions enter the sheath region with ion acoustic velocity. It is observed that all components of the velocity waves are damped in plasma in the time scale of one second. The computed oscillatory part of ion velocity match with the equation of the damped harmonic oscillator. Thus obtained damping constants as well as the frequency of all three components are nearly equal for obliqueness less than 600 after which they are distinctly different. This is due to the fact that the magnetic field becomes almost parallel to the wall. In earlier studies, only the final velocity profiles are reported and hence this study is useful in understanding how the ion velocities evolve in time as they move from sheath entrance towards the wall.

Carbon coated silicon nanoparticle is regarded as a promising anode material for the next generation of lithium ion batteries, while the development of a cost-effective and environmental-friendly preparation method is still difficult and hinders the practical implementation. In this research, a controllable and byproduct-free synthesis method is proposed for the preparation of silicon nanoparticles with amorphous hydrogenated carbon coating. The current apparatus is operated based on the application of induction thermal plasma. Plasma properties are tunable by adjusting the ratio of tangential and radial gas flow rates (T/R), which compose the plasma sheath gas. Obtained results reveal the plasma shape is shrunk with higher T/R values, which will lead to a steeper temperature gradient and lower temperature distributions in reaction chamber. Consequently, the compositions and properties of synthesized particles can be modified with T/R values. The formation of SiC, which was an intractable issue before, can be vanished at higher tangential gas flow rates in current research and the capacity of silicon anode for batteries will be improved in predict. This research is significant for a deep understanding of plasma synthesis processing and design of batteries with excellent performance.

The plasma sheath, which is the weakly ionized gas layer that envelopes hypersonic vehicles in near space, could shield communication signals and yield communication blackout. In the recent couple of decade, the extremely high frequency (EHF) communication is being considered as a potential solution to the blackout problem. On the other hand, previous studies used to focus on the EHF wave propagation in idealized plasma slabs or plasma sheaths covering blunt-coned vehicles. In the present letter, the plasma sheath enveloping sharp-coned hypersonic vehicles was modeled. The characteristics of EHF wave propagation in the sharp-coned plasma sheath were investigated. According to the study, the maximum electron densities and electron collision frequencies in sharp-coned plasma sheath is in the same magnitude of that in blunt-coned plasma sheath. However, the thickness of sharp-coned plasma sheath is much lower than that of blunt-coned plasma sheath. In addition, the power transmission rate at the frequencies of 140 and 225 GHz is high enough to afford communication tasks. Moreover, the reflection plays important roles in the energy loss of EHF wave propagation in sharp-coned plasma sheath, whereas the reflection in blunt-coned plasma sheath is ignorable. According to the analysis, the reason for such difference is that the gradient of relative permittivity in sharp-coned plasma sheath is larger than that of blunt-coned plasma sheath, which yields significant reflection to the EHF waves.

The “black barrier” phenomenon caused by plasma sheath during the reentry of a high-speed target will seriously affect the detection of radar echo by a ground monitoring station, which is not conducive to making corresponding adjustments to different situations in real-time. The echo reflects the information of the target’s position and speed, which is significant for real-time monitoring and effective strike. In this work, the effect of a high-speed target plasma sheath on electromagnetic wave echo characteristics was investigated by using the proposed spatially inhomogeneous and time-varying plasma sheath model. The Z-transform finite-difference time domain (Z-FDTD) method was adopted to calculate the time domain and frequency domain results of the echo in plasma sheaths with spatially inhomogeneous, uniform and spatially inhomogeneous and time-varying electron density distributions. The effects of different time-varying parameters and plasma parameters on the echo characteristics of the plasma sheath were analyzed. The results show that the reflected echo in spatially inhomogeneous and time-varying plasma is less than that of the other two. The magnitude of the reflected echo is proportional to the time-varying parameter peak coefficient and Gaussian width, and inversely proportional to the collision frequency and plasma thickness. The theoretical results provide important guidance for ground monitoring and anti-stealth.

Mayenite electride has attracted increasing research interests because of its unique electronic properties. The thermionic emission behavior of the mayenite electride is relatively unknown. Previous studies revealed that mayenite electride exhibited a bare work function ranged from 2.1–2.6 eV when the thermionic emission was tested in vacuum, and enhanced emission currents could be achieved by applying a super-high external electric field. In this paper, the thermionic emission behavior and the corresponding effective work function of two types of mayenite electride based composites, mayenite electride-titanium and mayenite electride-carbon, were investigated in an Ar glow discharge plasma at elevated temperatures (400–1000 K) without applying a high external electric field, which is critical for the application in electric propulsion and other aerospace apparatus, yet never had been done before. During the testing, the thermal equilibrium process and plasma sheath expansion were observed. The effective work function of the two mayenite electride composites were determined as a function of temperature. The Rasor-Warner model was applied to determine the bare work function and adsorption-site density of the mayenite electride based composites. Results suggested that the adsorption of Ar ions led to the enhanced thermionic emission (~30 A/m2 at 985 K) and low effective work functions (0.9–2.2 eV) of mayenite electride based composites, without the need of applying high electric fields. Our findings will pave the ways for the application of mayenite electride and its composites as the thrust cathode materials for electric propulsion where plasma is present.

To date, plasma sheath effects have not been incorporated into most CFD simulations of magnetohydrodynamics (MHD) or aerothermodynamics due to the high computational costs involved. The accurate mo...

A new electromagnetic (EM) calculation model, the inhomogeneity zonal medium model (IZMM) (based on the physical optics (PO) method), is proposed to calculate and analyze the EM scattering characteristics of hypersonic vehicle covered with a plasma sheath. First, the flow field of the plasma sheath is divided into nonuniform calculation subregions with different spacing sizes. The shape of the external flow field of the aircraft is modeled by fitting with a paraboloid and circular platform with different radii. Then, the electron density, temperature, and pressure distribution are obtained by collecting data from different points in the flow field of the sheath. Finally, a piecewise PO method is used to calculate the backscattering radar cross section (BRCS) of the hypersonic vehicle covered with plasma sheath from $L$ -band to $X$ -band. The numerical results show that the EM scattering characteristics of a target spacecraft covered with a plasma sheath can be described more accurately by using zoned medium model simulation. Under different flying conditions, the BRCS of hypersonic vehicle covered with a plasma sheath appears to be reduced to different degrees in the $S$ -band and the band range of 7–11 GHz, and a large attenuation of BRCS occurs in the head area of the aircraft. The research results enrich the EM modeling method of hypersonic vehicles, overcome some shortcomings of the existing PO method, and provide technical support and innovative ideas for the accurate analysis of the EM scattering characteristics of hypersonic targets.

A 2D computational model, incorporating the Snowplow approximation in the mass balance, is used to simulate the acceleration of an annular current sheath along two coaxial electrodes, with the inner one having either cylindrical or conical shape. The circuit, mass and momentum equations are simultaneously solved in 2D (r, z) considering initial breakdown along the insulator surface, ideal gas mass accretion by the current sheath (snowplow model) and distributed inductance along a coaxial transmission line short-circuited by the current sheath. Plasma density and electron temperature in the current sheath are estimated using standard planar shock theory. Numerical integration of the model’s equations for a given electrode geometry yields the temporal evolution of the current sheath parameters during the axial acceleration phase. In order to see the effect of the inner electrode shape on sheath parameters (i.e. transit time, kinetic energy, total mass, shape, etc.) and/or circuit properties (i.e. circuit inductance, voltage and current evolution, etc.), the portion of the inner electrode beyond the insulator was given a conical shape. By changing the cone slant in a range between ±5°, it was found that the current driven on the plasma sheath varies nonlinearly with the angle. The divergent (positive angle) electrode gives the sheath the highest kinetic energy, being twice the value corresponding to that of the straight inner electrode case, and the transit time is reduced from 1.34 to 1.20 µs. The estimates of plasma density and electron temperature indicate that the achievable ion densities are on the order of 4x1022 m-3, which corresponds to 30 % ionization, and typical temperatures at the end of the rundown phase are on the order of 8 eV. These values are comparable with those measured in experimental devices. The development of this tool will enable us to benchmark its results against an experimental installation currently close to being operational, and a future follow-up paper will be devoted to the comparison between the prediction of the rundown phase behavior and experimental results utilizing conical electrodes.

The understanding of ion dynamics in magnetized plasma sheath is crucial for all applications of plasma. The velocity variation as well as modulation frequency of ions in a magnetized plasma sheath has been studied for different obliqueness of the magnetic field. The governing Lorentz force equation has been solved numerically for the given boundary conditions as applicable in the kinetic simulation of the sheath. For different obliqueness of the magnetic field, the average values, maximum amplitude, damping factor as well as frequency of oscillation are studied. The oscillating velocity components change at different rates depending on their orientation with respect to the field direction. Significant changes in the damping factor and modulation frequency has been observed for all components of velocity; however, the frequency of oscillation remains the same. As the obliqueness increases, shoulder natures in the components of velocity are observed. BIBECHANA 18 (2021) 134-139

Nanostructuration and 2D patterning of thin films are common strategies to fabricate biomimetic surfaces and components for microfluidic, microelectronic or photonic applications. This work presents the fundamentals of a surface nanotechnology procedure for laterally tailoring the nanostructure and crystalline structure of thin films that are plasma deposited onto acoustically excited piezoelectric substrates. Using magnetron sputtering as plasma technique and TiO2 as case example, it is demonstrated that the deposited films depict a sub-millimetre 2D pattern that, characterized by large lateral differences in nanostructure, density (up to 50%), thickness, and physical properties between porous and dense zones, reproduces the wave features distribution of the generated acoustic waves (AW). Simulation modelling of the AW propagation and deposition experiments carried out without plasma and under alternative experimental conditions reveal that patterning is not driven by the collision of ad-species with mechanically excited lattice atoms of the substrate, but emerges from their interaction with plasma sheath ions locally accelerated by the AW-induced electrical polarization field developed at the substrate surface and growing film. The possibilities of the AW activation as a general approach for the tailored control of nanostructure, pattern size, and properties of thin films are demonstrated through the systematic variation of deposition conditions and the adjustment of AW operating parameters. Ministerio de Ciencia e Innovación PID2019-110430GB-C21 Junta de Andalucía P18-RT-3480 European Union 899352

The understanding of the properties of magnetized plasma sheath has been various beneficial applications in surface treatment, electron emission gun, ion implantation, and nuclear fusion, etc. The effect of electron temperature on the magnetized plasma sheath has been studied for a fixed magnetic field and ion temperature. It has been observed that various plasma sheath parameters can be prominently altered by the varying temperature of the electron. The density of ion is influenced more by the change in electron temperature rather than the electron density. The temperature of the electron has a great effect at the wall, when electron temperature increases, the ion and electron densities at the wall decreases. This shows the potential at the wall also decreases follows the Poisson’s equation. Similarly, the electric field also decreases but total charge density increases when the electron temperature is increased. BIBECHANA 18 (2021) 58-66

Terahertz (THz) communication has always been considered as a potential solution for “communication blackout” during aircraft reentry. In this article, the propagation characteristics of the THz wave in the realistic plasma sheath during the whole reentry process are studied by solving the fluid model and the THz transmission model. As a result, the electron number density and collision frequency decrease with the increase of reentry height and antenna position. And the attenuation of the THz wave decreases with the increase of the electromagnetic (EM) wave frequency, reentry height, and antenna position. Finally, two THz communication schemes to mitigate or avoid the “communication blackout” problem for the whole reentry process were discussed. One is for uncertain antenna position and reentry height, selecting EM waves with a frequency above 0.35 THz for communication. The other is to install the antenna near the bottom of the vehicle ( $L = - 1.0$ m in this article) with a wave frequency above 0.12 THz.

Plasma sheath, which forms between a material wall and incoming plasma, plays an important role in controlling particle and energy fluxes to the wall. The problem of plasma sheath is one of the oldest in plasma and still draws attention, especially in magnetized plasmas. In this work velocity of ions in a magnetized plasma sheath has been studied using a kinetic trajectory simulation model for varying obliqueness of the field. Any change in obliqueness of the field causes the velocities to change. The change in mean value of the component normal to the wall is comparatively small whereas the other two components of velocity vary sinusoidally, nearly complementary to each other with nearly equal amplitudes.

The high velocity of the re-entry object causes its surface to be enveloped with a plasma sheath. In the process of target detection of re-entry objects, the plasma sheath with fluid characteristics results in multiple reflected signals in the radar echo. Multiple targets appear in the 1-D range profile following pulse compression processing of a multicomponent echo signal. We refer to targets different from the real target as interference targets. The appearance of interference targets seriously affects the radar detection of re-entry objects, resulting in positioning failure or even tracking loss. In this article, by establishing the physical model of radar echo with multiple reference points and multiple velocity parameters of the re-entry object under plasma sheath, the multitarget phenomenon of the re-entry target echo signal on the 1-D range profile is simulated. A target detection method based on Doppler frequency compensation and nonuniform plasma sheath reflection model is proposed, which can effectively suppress false targets and realize reliable detection of targets under plasma sheath. The feasibility of detecting a target enveloped by a plasma sheath is verified by simulation, laying the foundation for the precise detection and tracking of targets.

The surface of a hypersonic vehicle traveling at a speed exceeding Mach 10 is covered by a plasma sheath. The plasma sheath is a complex dynamic random medium that seriously attenuates electromagnetic (EM) waves and generates the so-called blackout phenomenon. However, owing to changes in vehicle flight parameters, such as the angle of attack, speed, and altitude, or the effects of plasma weakening control measures, the attenuation effect of the plasma sheath on EM waves weakens for a short time. At times, the amplitude of the EM waves is higher than the communication threshold, and the EM waves penetrate the plasma sheath in a so-called “communication window”. However, the random temporal variance of the plasma sheath parameters causes the required parameters of the “communication windows” to appear randomly, resulting in the traditional communication methods that needs to keep the communication link open for a long time being no longer applicable. To maximize the use of these “communication windows”, this paper proposes a short-frame fountain code (SFFC), constructs a time-varying plasma sheath channel model, and studies the relationship between the SFFC parameters and the transmission performance of this particular channel. Simulation and experimental results show that the use of SFFC improves the reliability of communication through the plasma sheath. The uninterrupted and correct transmission of information can be achieved even when the plasma equivalent frequency is close to the carrier frequency.

Plasma–surface interactions caused by electric propulsion devices are an important spacecraft aspect of the design that is difficult to measure in ground-based facilities. The negatively biased solar panel surfaces attract the slow-moving charge exchange (CEX) ions generated inside an ion core plume, which can cause surface sputtering on the protective coatings of the solar panels. We use a fully kinetic particle-in-cell direct simulation Monte Carlo (PIC-DSMC) approach that models both electron and ion trajectories to allow us to fully characterize the plasma sheath formed near these surfaces and to understand how the plasma sheath affects the trajectories of CEX ions, their incident energies and angles, and surface sputtering rates. We find that, outside the plasma core, the ion and electron distribution functions are highly non-Maxwellian, and the assumption of electron temperatures is questionable. We introduce a novel floating potential ground boundary condition that enables us to emulate the spacecraft ground for a high range of plasma number densities and surface charging conditions. Finally, we estimate the erosion of the surface using the kinetic results and surface yield empirical relations.

Turbulence in the plasma sheath around reentry vehicles is known to contribute to radio-communications blackout, but a practical laboratory model of that extreme environment remains elusive. Herein, we present a table-top plasma system with sustained, chaotic convection for that purpose. Strong sound waves exert acoustic radiation pressure on gradients within the plasma and are shown to drive sufficient convection to cause abrupt and chaotic variation in the plasma properties. The volume-averaged plasma conductivity and collision time are determined in real time by phase-sensitive detection of a microwave probe signal. The experiment provides unique opportunities to study transmission into plasma conditions that can inform detailed models of high-temperature turbulent flows.

Terahertz communication is considered as a potential solution to alleviate the communication blackout. However, it is not clear how the shape parameters of the vehicle affect the propagation of terahertz communications in the plasma sheath. In this article, the influence of half-angle on the plasma flow and terahertz propagation characteristics around blunt cone vehicle was investigated using the numerical hypersonic hydrodynamic model and multilayer transmission model. The maximum electron number density in the plasma sheath near the antenna decreases with the decreasing half-angle. The thickness of the high-density section in the plasma sheath is almost unaffected by the half-angle. As a result, the terahertz wave attenuation decreases with the decreasing half-angle. The half-angle is reduced from 20° to 5°, and the attenuation of electromagnetic waves is reduced by about 25 dB. Therefore, reducing the half-angle of blunt cone vehicle can effectively reduce the attenuation of electromagnetic waves. Finally, the feasibility of lowering the half-angle to solve the blackout problem during the whole reentry process was discussed; the results show the operating frequency of terahertz wave that maintains normal communication when the half-angle is 1° is reduced by 0.1 THz compared with the half-angle of 9°. Based on the study, a new scheme combining the reduction of half-angle of blunt cone vehicle and terahertz communication was proposed in this article to mitigate the RF blackout.

We investigate the quasi-neutral limit (the zero Debye length limit) for the Euler-Poisson system with radial symmetry in an annular domain. Under physically relevant conditions at the boundary, referred to as the Bohm criterion, we first construct the approximate solutions by the method of asymptotic expansion in the limit parameter, the square of the rescaled Debye length, whose detailed derivation and analysis are carried out in our companion paper [8] . By establishing H m -norm, ( m ≥ 2 ) , estimate of the difference between the original and approximation solutions, provided that the well-prepared initial data is given, we show that the local-in-time solution exists in the time interval, uniform in the quasi-neutral limit, and we prove the difference converges to zero with a certain convergence rate validating the formal expansion order. Our results mathematically justify the quasi-neutrality of a plasma in the regime of plasma sheath, indicating that a plasma is electrically neutral in bulk, whereas the neutrality may break down in a scale of the Debye length.

The phenomenon of radio blackout due to a plasma sheath during reentry has attracted much attention over the last several decades. However, radio blackout has long puzzled aerospace researchers and has not yet been completely resolved. Owing to the effects of the time-varying plasma sheath channel environment, the constellation of received signals exhibits multiple manifolds, making the traditional algorithms based on Euclidean distance unable to perform demodulation. In the current study, we proposed a novel demodulation method based on spectral clustering for phase-modulated signals interrupted by the plasma sheath channel. Experimental results revealed that as long as the receiving radio waves were above the floor of receiver’s dynamic range, the proposed algorithm effectively classified received signals after time-varying plasma. The parasitic modulation interference caused by time-varying plasma was restrained effectively through the novel algorithm. In contrast to the traditional communication method, the proposed method can be applied to telemetry, track and command, as well as communication between reentry vehicles and near-space hypersonic vehicles in future.

The results of the development of a two-dimensional MHD code for carrying out computational studies of the dynamics of plasma current sheath in spherical chambers with a plasma focus are presented. Equations of magnetohydrodynamics with allowance for magnetic field diffusion, thermal conductivity and plasma radiation are used in this work. An implicit scheme is used in the calculation of the magnetic field, which makes it possible to describe the motion of plasma in a low-density region behind the plasma sheath. The formulas that take into account the possible appearance of anomalous resistance in the plasma are used to calculate the plasma conductivity. The neutron yield is calculated with allowance for thermonuclear and beam–target neutron generation mechanisms. The effect of the minimum residual gas density behind the plasma sheath on the cumulation of the plasma sheath is studied. The effects of magnetic field diffusion, thermal conductivity and anomalous plasma resistance on the plasma sheath dynamics are considered. The calculations are performed for two spherical plasma-focus chambers operating with currents up to 1 and 2 MA and neutron yields to 1012 and 1.5 × 1013 DT neutrons, respectively. The comparison of the calculated dependences with experimental data on the current, voltage and neutron yield made it possible to refine the parameters used in the calculations and achieve a satisfactory agreement between the simulation and experiment.

The kinetic trajectory simulation method has been used to study ion velocity profile in a plasma sheath for varying magnetic field at fixed obliqueness. As the electrons have higher velocity compared to that of ions the wall is charged up negatively with respect to the core plasma. The negative potential then attracts the ions and repels electrons forming a thin positive space charge region in front of the wall. This positive space charge region, known as the ‘sheath’ separates the negatively charged wall from the quasineutral ‘presheath’ plasma. The ions moving towards the wall have to satisfy the Bohm criterion to ensure the stability of the overall plasma. The mean value as well as oscillation frequency of velocity of ions change as the magnetic field is varied from 1.5 to 10.5 mT. The maximum amplitude of normal component of velocity is almost independent of the magnetic field but the maximum amplitude of other components of velocity change and shows oscillating nature as the magnetic field changes.

Formations of complex structures observed during the instability instigated expanding capacitive mode of RF discharge in a linear vacuum vessel, in the absence of an externally applied magnetic field or any other additional constraint applied. Systematic measurements of the plasma parameters, using multiple probe diagnostics, carried out to investigate the parametric dependence of sheath development reveal visible cylindrical tube like multiple double-layer formations around a mesh-type cylindrical plasma source. Such firetube formations provide many interesting and vital information on expanding radio frequency (RF) plasma sheath, charge particle trapping and the associated sheath instability with the RF discharge. The sheath structures, glowing spot formations, space charge formations, complex structure and firetube formations in the expanding plasma are some of the features discussed here in relation to such an expanding RF discharge. Low-frequency sheath instabilities are also observed in connection to the firetube formations using a coaxial mesh-type cylindrical plasma source powered at an operating frequency of 13.56 MHz. The ion acoustic frequency-dominated instability is identified as a sheath-plasma instability associated with the RF plasma.

The “magnetic window” is considered to be an effective technique for alleviating a vehicle’s atmospheric reentry blackout, whereas the dynamic variation characteristic of the plasma sheath is critical for the vehicle’s communication. In this article, the effects of dynamic plasma sheath on electromagnetic wave propagation and the bit error rate (BER) of two typical modulation signals under an external magnetic field are investigated. First, the hybrid matrix method is used to calculate the transmission coefficients of right-handed circularly polarized (RHCP) waves with different magnetic fields and plasma electron density fluctuation. Then, the average BER of two typical modulations signals, namely M-ary phase-shift keying (MPSK) and noncoherent M-ary frequency shift keying modulation (NC-MFSK) is numerically simulated based on the magnetized plasma sheath channel response. The results show that the magnitude in dB scale and phase of the RHCP transmission coefficient follow Gaussian distribution when the probability density function of the electron density is a Gaussian distribution. The BER performance of binary phase-shift keying (BPSK) and NC-MFSK is relevant to the incident wave frequency, the plasma stopband, and the intensity of electron density variation. Owing to the insensitivity of phase jitter, the NC-8FSK has a better performance than BPSK, followed by NC-4FSK and NC-2FSK.

Corona discharges on conductors are unavoidable in high-voltage direct current (HVDC) transmission lines. The cross-section geometry of the conductor is an important factor which significantly affects the positive corona discharges of dc transmission lines. Here, an improved fluid model is proposed to simulate the dc positive corona discharges on conductors with different cross-section geometries. The evolution of electric field and plasma sheath of circular conductor and aluminum conductor steel reinforced (ACSR) has been demonstrated. It is shown that the cross-section geometry of the conductor mainly affects the corona characteristics at the start stage of the discharge, whereas it has little influence with the development of corona discharges. Moreover, the effects of cross-section geometries of the conductors on plasma sheath characteristics are also discussed. The results would provide guidance for the selection and design of conductor section in high-voltage overhead transmission lines, which may find wide applications in the diagnosis of corona effects on the surface of conductors.

A 3-D total-field/scattered-field (TF/SF) plane-wave source was developed for the analysis of the plane wave propagation characteristics in the reentry plasma sheath. Owing to the dynamic variation in the surrounding flow field, the plasma sheath during the reentry process presents various 3-D inhomogeneous structures, such as dynamic plasma turbulence and considerable metal ablation particles. The proposed 3-D model can be efficiently applied to simulate the scattering effects of the 3-D inhomogeneous structures on the electro-magnetic (EM) signals. The proposed model utilizes a 3-D TF/SF boundary to introduce the plane wave source into the simulation domain, and six pairs of 2-D auxiliary propagators are created to generate the incident field on the TF/SF boundary based on the phase matching and the current density convolution finite-difference time-domain (JEC-FDTD) method. The uniaxial anisotropy perfectly matched layer (UPML) is modified as the absorbing boundary condition of the 2-D propagators. Implementation issues such as stability and dispersion are also discussed. The accuracy and efficiency of the proposed scheme are validated by admirable numerical simulation results and excellent agreement with the transmission line analogy method.

In this paper, the effect of particle trapping in a three-component plasma sheath model has been investigated analytically. The behavior of plasma sheath is studied with cold fluid ions, trapped/vo...

The evolution of sheath in plasma contaminated with varying dust charges under the effect of an external magnetic field is studied. Study of Sagdeev potential through pseudoptential approach has been attempted with a view to deriving the sheath equation. Numerical analysis has been carried out to study the potential variation with sheath-ward distance for various plasma parameters. A unique finding of the study is that the presence of dust particles as well as the magnetic field drastically modifies the Bohm sheath criterion for plasma sheath formation as obtained earlier in unmagnetised two-component plasma. The results have more realistic interpretation in showing explicitly the interaction of magnetic field and impurity caused by dust charge variation, with the possibility of its impact in various technological applications including plasma-material interaction, material processing and electro-mechanical devices.

We present an analysis of dynamic processes for the electromagnetic wave packet passing through the opaque media with quasi-free charges. We consider plasma sheath surrounding the spacecraft as it passes through the dense layers of the atmosphere. In order to provide effective tunneling of the signal to the receiving antenna, the dielectric “resonator” between the surface of the vehicle and plasma is supposed. We discuss the peculiarities of such radio frequency telecommunication channel and analyze in detail tunneling of the wave packet to the resonator and the decay processes for excited oscillations in the resonator. The peculiarities of tunneling through the nonstationary plasma layer are analyzed.

The aim of the present work is to develop a numerical model to understand and optimize the process parameters for the growth of carbon nanofibers (CNFs) inside the plasma enhanced chemical vapor deposition system containing acetylene, hydrogen, and argon gases. Two-dimensional axis-symmetrical inductive couple plasma module is implemented using COMSOL Multiphysics 5.2 simulation software to analyze the density profiles and temperatures of electrons, ions, and neutral species in the plasma at different gas pressures and input plasma powers. The outcomes of the COMSOL computational model show that the electron density in the plasma decreases with increase in gas pressure and increases with increase in plasma power. Other than the computational model, an analytical model is developed in the present paper that accounts the plasma sheath equations to study the fluxes and energies of the plasma species. The results obtained from the plasma sheath model at the catalyst-substrate surface boundary are fed as the input parameters to surface deposition model to investigate the growth characteristics of carbon nanofibers, i.e., poisoning of the catalyst nanoparticle, height, and diameter of carbon nanofiber at different gas pressures and input plasma powers. It is found that electron density decays at the faster rate when gas pressure is increased and decays at slower rate when input plasma power is raised. Moreover, it is also found that growth rate of CNFs increases with increase in gas pressure and plasma power. However, the significant drop in CNF growth rate is observed when the gas pressure is high enough (above and around 50 Torr). From the results obtained, it can be concluded that the CNFs having good growth characteristics can be obtained at some optimum pressure range, i.e., one order of the magnitude in the units of Torr. A good comparison between numerical simulation results and analytical results with each other and with existing experimental results confirms the adequacy of the computational and analytical approach.

The vertical spatial distribution of dust particles in radio frequency (RF) discharge plasma sheath is studied. The dust particles are levitated above the powered electrode in the discharge. From the distribution of the dust particles of different sizes generated by mixing of suitable gases, the effect of changing the RF power on the dust cloud behavior is studied. It is found that the distribution of the different sized dust particles in the sheath with variable bias differs significantly from that of single sized dust particles with fixed bias. As the RF power increases, the distribution range as well as the levitation height of the dust cloud above the powered electrode decrease. A theory for the observed results is also given. Based on the experimental and numerical results, we attribute the observed dependence to a combination of the enhanced sheath electric field and the ion drag force, but the decrease of the sheath thickness with increase of the discharge power has only minor contribution.

Ion bombardment of electrodes in an electric vacuum device can induce high-voltage breakdown. In order to explain this phenomenon, we, for the first time, analyzed a typical model of protons impacting the electrode with the help of a particle-in-cell (PIC)-direct simulation Monte Carlo (DSMC) code. In this model, we considered both the secondary electron yield and the gas desorption from the electrode. The temporal and spatial distribution evolution of electrons, ions, and neutrals under different electrode conditions is presented. The critical value of local gas density to induce breakdown is 1025 m−3. According to the discussion of the formation of the electrons avalanche, the electron ionizing gas is the key component for affecting the formation of a breakdown, and the production of plasma sheath near the electrode greatly contributes to the electrons avalanche.

It is demonstrated that Mg, Cr, Mn and B can be doped close to GaAs surface by plasma doping without external bias at room temperature (RT). The process only takes a few minutes, and impurity densities in the range of 1018–1021/cm3 can be achieved with doping depths about twenty nanometers. The experiment results are analyzed and the physical mechanism is tentatively explained as follows: during the doping process, impurity ion implantation under plasma sheath voltage takes place, simultaneously, plasma stimulates RT diffusion of impurity atom, which plays the main role in the doping process. The enhanced RT diffusion coefficients of Mg, Cr, Mn and B in GaAs are all in the order of magnitude of 10-15 cm2sec-1. This is reported for the first time among all kinds of plasma assisted doping methods.

Research on the dynamic properties of a plasma sheath coupled with pitching motion of the vehicle has great significance in solving the problem of communication interruption in the process of vehicle reentry. This paper investigates the dynamic properties of the plasma sheath by using the simplified conventional Burnett (SCB) equations and the Navier-Stokes (NS) equations with the thermochemical non-equilibrium effect. The eleven-species chemical kinetic models are applied to the comparison and there is verification of a dynamic plasma sheath simulation for the first time. After the introduction of vehicle pitching motion, the dynamic results are more consistent with the experimental data than the simulated results when treating it as static state. The plasma sheath characteristic parameters show periodic properties, whose changing period is the same as the pitching motion period. However, because of different velocities of the pitching motion, phase shifts exist in different positions of the vehicle. The enhancement of the rarefied effect weakens the disturbance to the plasma sheath. This research reveals the distribution and regularities of the dynamic plasma sheath. It is significant in solving the ionization blackout problem and the design of the reentry vehicle, and provides reliable data for further research on the dynamic plasma sheath.

Generation of metal plasma in vacuum arc discharge is always accompanied by a production of macroparticles (MPs). The MP contamination in coatings is the most important technological problem in plasma immersion ion implantation (PIII). For the case of PIII with long pulse duration, the results of theoretical study of MP charging and dynamics in the plasma sheath are presented. To describe the MP charging in the sheath the sheath model is combined with orbital motion limited (OML) theory. The MP charging in the sheath is studied with taking into account emission processes from MP surface as well as kinetic electron emission (KEE) from the high voltage substrate. The charge and dynamics of MP are governed by local parameters of counter fluxes of ions and secondary electrons from the substrate. The MP charge depends on the MP local position within the sheath. The dominant role in MP charging is shown to be played by KEE from the substrate, which is an important feature of PIII. KEE from the substrate changes the potential profile within the sheath, the sheath thickness, and current balance on MP surface. MP charge is obtained to be negative because it is caused by higher current density of secondary electrons from the substrate than that of ions. The latter is possible for KEE yield larger than a unit. The substrate biasing influences both the release of secondary electrons from the substrate under ion impact and their acceleration in the sheath. The increasing of negative substrate bias is demonstrated to result in the increasing of absolute value of negative MP charge, and, thereby, the increasing of electrostatic reflection of MP from the substrate. The negative substrate biasing is shown to be the effective alternative method to reduce MP contaminations in coatings without applying any magnetic filters.

Hypersonic velocities can theoretically affect the propagation of electromagnetic waves in a plasma sheath covering a vehicle. This article is the continuation of our previous study and, for the first time, investigates the reflection characteristics of electromagnetic waves by a moving bounded plasma slab and examines five typical plasma parameters in detail when the plasma moves parallel to the interface. The results show that the motion of the plasma slab significantly affects electromagnetic propagation, and the reflection coefficient oscillates with the velocity of the plasma sheath. In addition, different physical parameters cause different oscillation characteristics. Various interesting features of the reflection coefficient are obtained, which are very important for researching the propagation of electromagnetic waves in this extreme physical environment or providing reference for researching “blackouts” in the future.

In this paper, the problem of sheath is investigated using the fluid model in a magnetized four-component dusty plasma system comprising positive ions, negatively charged statistic dust grains and two species of electron populations. These electrons are assumed to be a sum of two q-nonextensive electrons distribution (i.e. the electrons evolve far away from their Maxwellian distribution ( q = 1 ) with two different temperatures (cold and hot). The effects of population ratio and the temperature ratio of hot to cold non-extensive electrons on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath as sheath thickness, sheath potential, electron and ion densities and dust velocity in the presence of nonextensively (case superextensively) distributed two-temperature electrons.

Sheath region of an electronegative magnetized plasma consisting of q-nonextensive electrons, Boltzmann distributed negative ions and positive ions with finite temperature is investigated by using a steady state fluid model. Considering Sagdeev's pseudo potential method, a modified Bohm criterion is derived. Taking into account the new formation criterion, the fluid model is then solved numerically and the density distribution of charged particles in the sheath region is studied for different values of the initial positive ion velocity at the sheath edge.

Modeling wideband plane-wave propagation through a stratified magnetized plasma sheath is important toward predicting the quality of communications during re-entry, scattering caused by electron density perturbations, and many other applications. When using the finite-difference time-domain (FDTD) method to solve the problem, modeling the incident field in the simulation domain is difficult if the incident field travels obliquely to the grid axes. In this article, a total-field/scattered-field (TF/SF) formulation whereby a plane-wave source is introduced into cold layered magnetized plasma has been developed for the FDTD method. Based on phase matching theory, twelve auxiliary 1-D propagators are specified to calculate the correction field values for the TF/SF boundary. A modified convolution perfect match layer (CPML) is implemented to terminate the 1-D propagators. Numerical results are also presented to show the accuracy and effectiveness of the method. Although this method is developed for magnetized plasma, the extension to other anisotropic dispersive layered media is straightforward.

The main purpose of the present work is to study the behavior of sheath properties in unmagnetized collisional plasma. The plasma consists of neutral atoms, thermal positive ions and non-extensive electrons. The ions are described by fluid model approach, while the electrons are considered following the q-non-extensive distribution and obey the Tsallis statistics. In this study, a steady state one-dimensional fluid model based on the ion continuity and momentum transport equations, in presence of source term, coupled to the Poisson’s equation and non-extensive electrons density equation is developed. The modified Bohm sheath criterion is also determined and studied. The numerical results obtained highlight the effect of the nonextensivity q-parameter and the positive ion temperature on the evolution of the quantities characterizing the plasma sheath, such as charged particles densities, ion velocity, electric potential and sheath thickness. It is seen that as the q-parameter increases, the charged particles densities decrease more rapidly in the sheath region while the normalized electric potential increases strongly, which leads to a significant decrease in sheath thickness. It is also shown that by increasing the ion temperature for constant q, or by increasing the value of q-parameter for constant ion temperature, the ion velocity increases significantly in the sheath.

Diagnostics of plasma–wall interaction processes provide important information on nuclear fusion devices. Elucidation of the charge state distribution and temporal evolution of multi-charged ions is essential to improve laser ablation-based diagnostics of the plasma–wall interaction processes. Molybdenum is a material of interest in fusion and has been used as the plasma-facing material of the first wall in the EAST tokamak. In this work, the dynamic characteristics of multi-charged ions emitted from a molybdenum plasma produced by a Q-switched Nd:YAG nanosecond laser (wavelength 1064 nm, pulse width 7 ns) were studied using time of flight mass spectroscopy under a pressure of 6 × 10−4 Pa. The charge state distribution and temporal evolution of the multi-charged ions at various laser power densities from 0.85 GW cm−2 to 7.9 GW cm−2 were systematically investigated. This power density range is commensurate with that used in LIBS and LIAS diagnostics of the plasma–wall interaction process in EAST tokamaks. The ion charge state was found to increase with laser power density and the observed maximum charge state was up to seven at the highest laser power density used in these experiments. The higher charged ions had greater velocities indicating that separation took place between the different charged ions during the plasma expansion process. The origin of multi-charged ions is attributed to step-wise ionization due to plasma shielding from strong laser absorption in the plasma and the reduction of the ablation rate with the increase in laser power density. The velocities between these multi-charged ions were related to the acceleration of the transient plasma sheath during the laser interaction with the target and plasma.